Results and Spatial Analysis

Code

library(tidyverse)
library(sf)
library(tidycensus)
library(tigris)
library(spdep)
library(INLA)
library(BMA)
library(leaflet)
library(plotly)
library(dplyr)
library(DT)
library(kableExtra)
library(corrplot)
library(car)
library(viridis)
library(patchwork)
library(ggtext)
library(tidyr)
library(ggplot2)



# Set global options
options(tigris_use_cache = TRUE)
sf_use_s2(FALSE)

knitr::opts_chunk$set(
  echo = TRUE,
  message = FALSE,
  warning = FALSE,
  fig.align = "center",
  cache = TRUE
)

1 Empirical Results: Capability Deprivations

This chapter presents the main results from the INLA-BYM2 spatial analysis.

A one-unit increase in the DIESELPM (Environmental) is associated with approximately a 494.7% increase in the correctional population
Census Response: -73.6 Strong negative relationship ➡️ Suggests community engagement & collective efficacy matters!
Automobile access: -91
Homeownership: -40.8
Bachelor’s Degree: -88.4, Significant spatial clustering
Education-employment interaction

Credible Intervals:

- 95% probability that the true parameter lies within a specific range, given the data
- Not significant: Not statistically significant (CI crosses zero). Very small effect size

Key Effects on Supervision Rates

Environmental conditions (+494.7%)
Transportation barriers (-91.0%)
Educational access (-88.4%)
Healthcare availability (-73.3%)

Interpretation

Place strongly shapes outcomes
Multiple barriers compound
Resources matter significantly
Context affects success

2 Targeted Strategies: High-Risk Areas (Negative ui)

Resource Development
- Expand treatment options
- Increase job programs
- Improve transportation
- Build support systems

Barrier Reduction
- Address access issues
- Enhance coordination
- Develop infrastructure
- Strengthen networks

3 Relative Risk: Results Visualization and Policy Translation

Spatial Patterns: Relative Risk Mapping

3.0.1 Relative Risk: Air Pollution

Relative Risk values > 1, this means there is higher risk than expected. Areas with higher RR values likely have more Diesel Particulate Matter than expected. 2.42 in Carbon County, then there is 142% more correctional population than expected. Or a place like Morgan county is 0.21 RR has 79% lower correctional population than expected which likely represents an area with better air quality.

Map Interpretation

Red areas: Higher than expected correctional supervision rates (RR > 1.5)
Yellow areas: Near expected rates (RR 0.8-1.2)
Light areas: Lower than expected rates (RR < 0.8)
Pattern significance: Spatial clustering suggests collective capabilities matter

“Areas with poor air quality show 147% higher correctional supervision rates, suggesting environmental conditions may be an important upstream factor in justice system involvement” * Census tracts with poor air quality have 2.42 times higher risk of elevated correctional populations * For areas with similar characteristics but better air quality, this tract shows 147% higher correctional supervision rates * Air quality appears to be a significant environmental risk factor associated with correctional supervision rates

Potential Pathway: Poor Air Quality → Health Issues → Economic Stress → Community Instability → Higher Supervision Rates

Contributing Factors: 1. Health impacts affect employment 2. Medical costs create financial strain 3. Environmental stress on communities 4. Reduced outdoor activities/community engagement

3.1 Key Findings: Environmental Justice and Capabilities

3.1.1 Primary Finding: Air Pollution Impact

Major Discovery:

A one standard deviation increase in diesel particulate matter is associated with a 494.7% increase in correctional supervision rates, even after controlling for poverty, demographics, and other factors.

Capabilities Interpretation:

Air pollution serves as a powerful environmental conversion factor that constrains capability formation through:

Health impacts affecting employment stability
Environmental stress reducing community cohesion
Disproportionate burden on low-income communities
Compound effects with other environmental hazards

4 Environmental Conditions as Conversion Factors

4.1 Relative Risk: Air Quality Impact on Supervision

Relative Risk (RR) becomes a measure of capability deprivation in space. Combines fixed and random effects. Accounts for spatial structure.

exp(α + Σβjxij + ui + vi)

RR > 1, this means there is higher risk than expected. Areas with higher RR values likely have more Diesel Particulate Matter than expected. High RR clusters → capability deprivation (RR = 1: Expected risk level. RR < 1: Lower risk than expected)
2.42 in Carbon County, then there is 142% more correctional population than expected. Or a place like Morgan county is 0.21 RR has 79% lower correctional population than expected which likely represents an area with better air quality.

4.1.0.1 Pathway to Supervision

Direct Health Effects
- Increased stress
- Physical health impacts
- Mental health strain
- Cognitive effects
Economic Impact
- Healthcare costs
- Work disruption
- Medical expenses
- Employment stability
Social Consequences
- Reduced outdoor activity
- Limited community engagement
- Restricted social networks
- Decreased collective efficacy

4.2 Geographic Distribution

4.2.1 Clustering Effects

Environmental hazards concentrate spatially
Poor air quality clusters with other disadvantages
Health impacts compound over time
Community capabilities constrained

4.2.2 Relative Risk Interpretation

RR > 2.0: Severe capability constraint
RR 1.5-2.0: Moderate impact
RR < 1.0: Better environmental conditions “Areas with poor air quality show 147% higher correctional supervision rates, suggesting environmental conditions may be an important upstream factor in justice system involvement”
Census tracts with poor air quality have 2.42 times higher risk of elevated correctional populations
For areas with similar characteristics but better air quality, this tract shows 147% higher correctional supervision rates
Air quality appears to be a significant environmental risk factor associated with correctional supervision rates

Potential Pathway: Poor Air Quality → Health Issues → Economic Stress → Community Instability → Higher Supervision Rates

Contributing Factors: 1. Health impacts affect employment 2. Medical costs create financial strain 3. Environmental stress on communities 4. Reduced outdoor activities/community engagement

5 Statistical Results

6 Spatial Components

Code

spatial_components <- data.frame(
  Component = c("Structured (Phi)", "Precision (re_u)", "Precision (re_v)"),
  Value = c(0.594, 2.79, 21100),
  Interpretation = c("59.4% spatial structure",
                    "Strong spatial dependence",
                    "Low unstructured variation")
)

DT::datatable(spatial_components,
              options = list(pageLength = 5),
              rownames = FALSE)

6.0.1 Protective Factors: Access and Engagement

Code

protective_data <- data.frame(
  Factor = c("Census Response\n(Community Engagement)", 
             "Automobile Access\n(Transportation)", 
             "Health Insurance\n(Healthcare Access)",
             "Employment Rate\n(Economic Opportunity)"),
  Risk_Reduction = c(73.6, 91.0, 72.6, 50.0),
  Theory_Connection = c("Collective Efficacy", "Mobility Access", "Health Security", "Economic Stability")
)

ggplot(protective_data, aes(x = reorder(Factor, Risk_Reduction), y = Risk_Reduction, 
                           fill = Theory_Connection)) +
  geom_col(alpha = 0.8) +
  geom_text(aes(label = paste0("-", Risk_Reduction, "%")), 
            hjust = -0.1, size = 4, fontface = "bold") +
  coord_flip() +
  scale_fill_viridis_d(option = "plasma", alpha = 0.8) +
  labs(x = "Conversion Factor", 
       y = "Risk Reduction (%)",
       title = "Protective Conversion Factors",
       subtitle = "How access and engagement reduce correctional supervision risk",
       fill = "Theoretical Domain") +
  theme_minimal() +
  theme(text = element_text(size = 12))

6.0.2 Implementation Focus

Target highest-need areas
Address multiple barriers
Build community capacity
Enhance coordination

--- title: "Results and Spatial Analysis" format: bookup-html --- ```{r inla-setup} library(tidyverse) library(sf) library(tidycensus) library(tigris) library(spdep) library(INLA) library(BMA) library(leaflet) library(plotly) library(dplyr) library(DT) library(kableExtra) library(corrplot) library(car) library(viridis) library(patchwork) library(ggtext) library(tidyr) library(ggplot2) # Set global options options(tigris_use_cache = TRUE) sf_use_s2(FALSE) knitr::opts_chunk$set( echo = TRUE, message = FALSE, warning = FALSE, fig.align = "center", cache = TRUE ) ``` ```{r data-import, include=FALSE} # Import spatial data library(sf) model_data_hpi <- st_read("data/model_data_hpi.shp") ``` # Empirical Results: Capability Deprivations This chapter presents the main results from the INLA-BYM2 spatial analysis. ```{r, echo=FALSE, fig.align = 'center', out.width="100%"} knitr::include_graphics("figures/Significant.png") ``` - A one-unit increase in the DIESELPM (Environmental) is associated with approximately a 494.7% increase in the correctional population - Census Response: -73.6 Strong negative relationship ➡️ Suggests community engagement & collective efficacy matters! - Automobile access: -91 - Homeownership: -40.8 - Bachelor's Degree: -88.4, Significant spatial clustering * Education-employment interaction Credible Intervals: - 95% probability that the true parameter lies within a specific range, given the data - Not significant: Not statistically significant (CI crosses zero). Very small effect size :::: {.columns} ::: {.column width="50%"} ### Key Effects on Supervision Rates {.unnumbered} - Environmental conditions (+494.7%) - Transportation barriers (-91.0%) - Educational access (-88.4%) - Healthcare availability (-73.3%) ::: ::: {.column width="50%"} ### Interpretation {.unnumbered} - Place strongly shapes outcomes - Multiple barriers compound - Resources matter significantly - Context affects success ::: :::: # Targeted Strategies: High-Risk Areas (Negative ui) :::: {.columns} ::: {.column width="50%"} 1. **Resource Development** - Expand treatment options - Increase job programs - Improve transportation - Build support systems ::: ::: {.column width="50%"} 2. **Barrier Reduction** - Address access issues - Enhance coordination - Develop infrastructure - Strengthen networks ::: :::: # Relative Risk: Results Visualization and Policy Translation Spatial Patterns: Relative Risk Mapping ### Relative Risk: Air Pollution *Relative Risk values > 1, this means there is higher risk than expected. Areas with higher RR values likely have more Diesel Particulate Matter than expected. *2.42 in Carbon County, then there is 142% more correctional population than expected. Or a place like Morgan county is 0.21 RR has 79% lower correctional population than expected which likely represents an area with better air quality. ```{r LEAFLET, echo=FALSE} pal <- colorQuantile(palette = "YlOrRd", domain = model_data_hpi$RR, n= 7) labels <- sprintf(" %s Observed: %s Expected: %s Air Pollution: %s SIR: %s Relative Risk: %s (%s, %s)", model_data_hpi$NAM, model_data_hpi$corr_pp, round(model_data_hpi$expectd, 2), model_data_hpi$dieslpm, round(model_data_hpi$SIR, 2), round(model_data_hpi$RR, 2), round(model_data_hpi$LL, 2), round(model_data_hpi$UL, 2) ) %>% lapply(htmltools::HTML) #LEAFLET MAPPING! lRR <- leaflet(model_data_hpi) %>% addTiles() %>% addPolygons( color = "grey", weight = 1, fillColor = ~ pal(RR), fillOpacity = 0.5, highlightOptions = highlightOptions(weight = 4), label = labels, labelOptions = labelOptions( style = list( "font-weight" = "normal", padding = "3px 8px" ), textsize = "15px", direction = "auto" ) ) %>% addLegend( pal = pal, values = ~RR, opacity = 0.5, title = "Relative Risk", position = "bottomright", labelFormat(transform = function(RR) sort(RR, increasing = TRUE)) ) lRR ``` ::: {.callout-note} ## Map Interpretation - **Red areas**: Higher than expected correctional supervision rates (RR > 1.5) - **Yellow areas**: Near expected rates (RR 0.8-1.2) - **Light areas**: Lower than expected rates (RR < 0.8) - **Pattern significance**: Spatial clustering suggests collective capabilities matter ::: "Areas with poor air quality show 147% higher correctional supervision rates, suggesting environmental conditions may be an important upstream factor in justice system involvement" * Census tracts with poor air quality have 2.42 times higher risk of elevated correctional populations * For areas with similar characteristics but better air quality, this tract shows 147% higher correctional supervision rates * Air quality appears to be a significant environmental risk factor associated with correctional supervision rates Potential Pathway: Poor Air Quality → Health Issues → Economic Stress → Community Instability → Higher Supervision Rates Contributing Factors: 1. Health impacts affect employment 2. Medical costs create financial strain 3. Environmental stress on communities 4. Reduced outdoor activities/community engagement ## Key Findings: Environmental Justice and Capabilities ### Primary Finding: Air Pollution Impact ::: {.theory-box} **Major Discovery**: - A one standard deviation increase in diesel particulate matter is associated with a **494.7% increase** in correctional supervision rates, even after controlling for poverty, demographics, and other factors. **Capabilities Interpretation**: Air pollution serves as a powerful **environmental conversion factor** that constrains capability formation through: - Health impacts affecting employment stability - Environmental stress reducing community cohesion - Disproportionate burden on low-income communities - Compound effects with other environmental hazards ::: # Environmental Conditions as Conversion Factors ## Relative Risk: Air Quality Impact on Supervision - **Relative Risk (RR) becomes a measure of capability deprivation in space.** Combines fixed and random effects. Accounts for spatial structure. ```latex exp(α + Σβjxij + ui + vi) ``` - RR > 1, this means there is higher risk than expected. Areas with higher RR values likely have more Diesel Particulate Matter than expected. **High RR clusters → capability deprivation** (RR = 1: Expected risk level. RR < 1: Lower risk than expected) - 2.42 in Carbon County, then there is 142% more correctional population than expected. Or a place like Morgan county is 0.21 RR has 79% lower correctional population than expected which likely represents an area with better air quality. #### Pathway to Supervision 1. **Direct Health Effects** - Increased stress - Physical health impacts - Mental health strain - Cognitive effects 2. **Economic Impact** - Healthcare costs - Work disruption - Medical expenses - Employment stability 3. **Social Consequences** - Reduced outdoor activity - Limited community engagement - Restricted social networks - Decreased collective efficacy ## Geographic Distribution ### Clustering Effects - Environmental hazards concentrate spatially - Poor air quality clusters with other disadvantages - Health impacts compound over time - Community capabilities constrained ### Relative Risk Interpretation - RR > 2.0: Severe capability constraint - RR 1.5-2.0: Moderate impact - RR < 1.0: Better environmental conditions "Areas with poor air quality show 147% higher correctional supervision rates, suggesting environmental conditions may be an important upstream factor in justice system involvement" * Census tracts with poor air quality have 2.42 times higher risk of elevated correctional populations * For areas with similar characteristics but better air quality, this tract shows 147% higher correctional supervision rates * Air quality appears to be a significant environmental risk factor associated with correctional supervision rates Potential Pathway: Poor Air Quality → Health Issues → Economic Stress → Community Instability → Higher Supervision Rates Contributing Factors: 1. Health impacts affect employment 2. Medical costs create financial strain 3. Environmental stress on communities 4. Reduced outdoor activities/community engagement # Statistical Results ```{r results-table, echo=FALSE} results_df <-read.csv("data/results_df.csv") DT::datatable(results_df, options = list( columnDefs = list(list(className = 'dt-center', targets = 5)), pageLength = 5, order=list(list(10,'desc')), lengthMenu = c(5, 10, 15, 20))) ``` # Spatial Components ```{r spatial-stats} spatial_components <- data.frame( Component = c("Structured (Phi)", "Precision (re_u)", "Precision (re_v)"), Value = c(0.594, 2.79, 21100), Interpretation = c("59.4% spatial structure", "Strong spatial dependence", "Low unstructured variation") ) DT::datatable(spatial_components, options = list(pageLength = 5), rownames = FALSE) ``` ### Protective Factors: Access and Engagement ```{r protective-factors-viz} protective_data <- data.frame( Factor = c("Census Response\n(Community Engagement)", "Automobile Access\n(Transportation)", "Health Insurance\n(Healthcare Access)", "Employment Rate\n(Economic Opportunity)"), Risk_Reduction = c(73.6, 91.0, 72.6, 50.0), Theory_Connection = c("Collective Efficacy", "Mobility Access", "Health Security", "Economic Stability") ) ggplot(protective_data, aes(x = reorder(Factor, Risk_Reduction), y = Risk_Reduction, fill = Theory_Connection)) + geom_col(alpha = 0.8) + geom_text(aes(label = paste0("-", Risk_Reduction, "%")), hjust = -0.1, size = 4, fontface = "bold") + coord_flip() + scale_fill_viridis_d(option = "plasma", alpha = 0.8) + labs(x = "Conversion Factor", y = "Risk Reduction (%)", title = "Protective Conversion Factors", subtitle = "How access and engagement reduce correctional supervision risk", fill = "Theoretical Domain") + theme_minimal() + theme(text = element_text(size = 12)) ``` ### Implementation Focus - Target highest-need areas - Address multiple barriers - Build community capacity - Enhance coordination